How I am simultaneously both: right, and probably, partly wrong…

[A few inline updates added, and some very minor copy-editing done at a few places, on 2014.12.28.]

In my research, I have found that I am simultaneously both right and, probably, partly wrong.

* * * * *   * * * * *   * * * * *

First, the probably partly wrong part. I will assume as if I am actually (partly) wrong, and write it. (The probability that I am wrong is very high.)

The error concerns my theory for the mechanism of propagation of photons that I had put forth almost a decade ago, formally published in Dec. 2005. I had had that idea since 1991/1992. The more recent experimental evidence, I guess, shows it wrong.

First, on to the mistake, and then, to the experimental evidence. [Here, I will not bother explaining myself. Instead, I will assume that you are well familiar with my published papers, know about the field, and thus, go straight-away to the heart of the matter.]

Ok. About the mistake. Essentially, it is that the mechanism that I had proposed implied that photons in free space have a diffusive dynamics. My browsing of the experimental evidence indicates that they instead have a ballistic dynamics. The theory, as presented in the papers, therefore, fails.

The experimental evidence comes from the PDC entangled photon pairs—i.e., if I get the evidence right.

Consider two PDC entangled photons. They are found at the intersection of the two cones. Assume that in experiment, the cones can be intercepted by detectors lying in a plane normal to the central axis, at any arbitrary distance. Suppose that the detectors’ plane lies at distance x_1 from the crystal and that you detect the entangled pair “simultaneously” at a certain time t_1. The question is, if the detectors’ plane is placed at a distance 10 x_1, what would be the detection time? If 10 t_1, then it obviously means that the dynamics is ballistic.

I presume that this in fact is the case in the actual experimentation, even though I could not easily find any direct experimental data to verify the same. But there is another reason why the dynamics must be ballistic.

If the dynamics were to be diffusive, then the probability of the simultaneously generated photon pairs ending up on the intersection spots would be so small that no one would think of producing photon pairs this way.

In my theory, the dynamics is diffusive because the photons change their directions randomly. This circumstance is impossible to realize in free space, because photons wouldn’t collide. By Pauli’s principle, two electrons would, but not two photons. Photons being bosons can occupy the same region of space without noticing each other.

[Update on 2014.12.28: The mistake isn’t “elementary.” Take two identical billiard balls and let them undergo perfectly elastic collision. The outcome is, in a way, the same as if two balls were to pass through each other without noticing the other’s presence. Think a bit more about this example and the mathematical (or “statistical”) in-distinguishability. … And also realize, despite Pauli’s principle, the mainstream QM doesn’t have anything to say on the matter: they don’t localize the photon while it is in propagation, in the first place. So, it’s not as if the issue has already been clarified by the physicists in their text-books and that the engineer is being audacious. BTW, most of the physicists who at all replied my emails, including an “Objectivist” one, had advised me to first study physics well, presumably before writing papers.]

Some further comments:

I myself detected the error; none else pointed out. Indeed, none else (say a student or a reviewer) even hinted at a possibility. Not a single physicist to whom I had on my own sent my paper, came up with this objection.

The only person(s) to raise any sort of objection here were, hold your breath, my thesis examiners! They had begun by asking me whether the simulation I performed was for electrons or photons. There had followed a string of questions on their part, and simple, examinee-like assertions (rather than logically most thoroughly sound answers) on my part. They had kept the matter in abeyance before moving on to the next set of questions.

Yes, IMO, they could have granted me a PhD.

The reason is, firstly, that I had worked very hard on it and therefore had ample other material to justify a PhD. (One of the examiners had noted the relatively unusually large volume of work submitted for the degree.) I had other work or observations or results concerning numerical modelling, Huygens-Fresnel principle, and diffusion equation, and some of it still looks very fresh and original to me even now (especially the last; more on it later, right in this post).

Secondly, even for wave-fields, the description I presented could still be used as an abstract model for simulation of other linear wave fields (and I had pointed out some of these applications right in my papers), though, now, not for photons in free space.

Thirdly, many of the non-mainstream assumptions which I explicitly made do not get invalidated by the current experimental evidence, and remain worth taking note of. These include identification of photon (i) as a spatially localized phenomenon or condition  (ii) in aether. To build a new theory is the whole point behind doing theoretical research. As a PhD student one must show that one has learnt if not mastered the art of working with fresh theoretical concepts in a logical, consistent, manner. I did show some ability in this regard, and this part of the work does not get much affected by a re-evaluation of the theory in the light of the fresh experimental evidence.

Fourthly, though now there remains little to my theory if it is taken as an integrated whole, the fact of the matter is, in the process of having worked hard to build a model that later on turns out to be erroneous, I learnt a lot even before the error could be detected. And, thus, presenting a better model would be far easier. Indeed to the experts I can already tell on the fly: For a universe consisting only of electrons as fermions and photons as bosons, a model whereby the fermion is the pollen-grain and the photons are the bumping particles can easily be built, after throwing in a set of rules to get the phases (including spin and chirality) right. [Update on 2014.12.28: And, of course, while writing this post itself, I did know that a clarification for the creation and annihilation operators would be necessary, too. I just forgot to mention it in the original post.] No, I am not going to rush building one immediately. I just wanted to point out how easy it becomes to build a new, consistent, theory. The required integrations are already there.

That’s why, even if I guess I will have to withdraw the theory, I call it as being only partly wrong.

[Update on 2014.12.28: I think I should still pursue obtaining precise experimental evidence, before formally withdrawing my theory.]

A few other notes:

I didn’t know about the PDC photons or their behavior when I built my theory. No researcher/reviewer pointed it out to me, perhaps because they didn’t make the connection themselves. Realize, in the absence of the knowledge of the ballistic dynamics of the PDC photons, mine is a perfectly sensible theory. The very words ballistic vs. diffusive is something I read for the first time while casually browsing the home page of the optics group at the Raman Research Institute last year or so. I still don’t know whether the terms technically apply the issue I outlined above, but still, presumably, I have made clear the error I made.

* * * * *   * * * * *   * * * * *

Now, on to the part where I am fully right. This, of course, concerns the diffusion equation.

The experiment that any one could perform at home (the one I hinted at, in my last post) consists of this one:

Take a blotting paper and put a small drop of blue ink in the centre. Watch the boundary separating the blue and white portions grow. [Yes, I know I have mentioned this experiment in my blog posts before. But now there is a bit of a new angle, so read on anyway.]

The Fourier theory does not acknowledge the existence of this front. In Fourier theory, the blueness is spread over the entire paper right from the word go.

If possible, make a video of the front, and find out the speed of the propagation of the front.

By arguments rooted in the numerical analysis methods, as well as by Einstein’s stochastic approach, the theory predicts a uniform speed of propagation for the front. (In Einstein’s theory, it’s stochastically uniform.) In Fourier’s theory, the concept is inapplicable and hence, if it at all must be used, then it can be said that the front has an infinite speed. [Since the blotting paper experiment does not fulfil all the requirements of the diffusion equation, your experimentally observed front may not have a uniform outward speed. But, the experiment does fulfil the aspect of a support limited to a sub-domain vs. that over the full domain.] [Update on 2014.12.28: Drop me a line if you want to perform a more complicated experiment that should conform to the diffusion equation better, at home or at school/college lab, and I will give you a few ideas.]

Here is another funny thing. Suppose the initial concentration/temperature profile is in the form of the cosine curve in between -\pi to +\pi, and that the domain also runs between the same limits. If you know Fourier’s theory, you know that essentially, we are simplifying the situation to the greatest extent by taking just a single basis function in the Fourier expansion (i.e., apart from the bias, which, for diffusion of mass, would have to be taken as -1 here).

Suppose further that the boundary conditions are maintained to be zero field variable (concentration/temperature) at both the endpoints.

Since the profile covers the entirety of the domain, the solution at every point, throughout the diffusion, would consist of only a cosine curve; it’s just that its height would go on dropping with exponential decay, as the diffusing species goes out of the domain.

Now, do a funny thing. Keep the initial profile as in the above example, but let the domain run from -10 \pi to +10 \pi.  The boundary conditions continue to remain the same: zero field variable.

If your intuition is like mine, we would expect the solution in the two cases to remain the same. But, in Fourier’s theory, they are not.

Since the domain size has increased, there is a portion 9 \pi long on each side of the initial profile that must be brought into the initial Fourier expansion. This introduces an infinity of basis functions into the initial profile. Naturally, the profile at any future time also is different from the first case.

[Update on 2014.12.28: I had also thought of mentioning the fact that the Fourier solution would be still different for a domain of total size \pm 2 \pi, but forgot to write about it in the original post.]

To a mathematician (and to any modern theoretical physicist—the same ones who can’t detect a mistake in my QM papers), the existence of different solutions for the same set of initial and boundary conditions, makes perfect sense. At least they don’t seem to notice anything amiss here. But what their position implies is the following, for your experiment at home.

If you take a bigger blotting paper, the shape of the solution should be different.

In other words, in Fourier theory, the solution crucially depends on the domain size, too—not just on the local dynamics of the diffusing species.

The experiment which I was going to request, would have made use of this domain-size dependence, for photons propagation. But then, as I said, I caught my own error, and so, I am not going to request performance of that kind of an experiment.

But what about the intuition, you say?

Well, if you take a local theory—Einstein’s stochastic, or those having roots in the numerical methods (and I need to give a name to these, just for convenience in reference)—the solution profile remains identical regardless of the domain size.

[Update on 2014.12.28: Indeed, you could even cut a significant portion of the paper near one of its edges after the diffusion has already begun, so long as the blue front has not reached that place, and it would still not affect the solution. I forgot to mention this point while writing the original version of this post.]

Getting more technical once again: There also is an implication for the instantaneous flux rate and the total outward flux, for the two theories. The local theories predict a zero flux until the front reaches the boundary. But since the diffusing species is conserved (conservation of mass or heat power, etc.), what it implies is that the local theories must give a faster flux rate at the times after the front reaches the boundary.

Keeping the conservation angle aside, the zero-flux state is something that should be easily verifiable in experiment. If it is experimentally verified, then, the local-physics theories win; else, the Fourier theory does.

I bet that the local theories would win. There is no blueness near the edges until the front travels there.

And, as far as I can tell, even if not photons, at least electrons do obey the diffusive dynamics in the free space. If careful experimentation is conducted, I predict (even ahead of building my new quantum theory) that there should be an experimentally verifiable zero-flux period, in contradiction to the mainstream quantum mechanics. And if it is observed, then it means that many mainstream ideas—or their mystifying components, at least—are completely wrong.

For this very reason, I don’t expect them to conduct the necessary experimentation with electrons. Or, try to think of any novel experimentation scheme with PDC photons.

In the meanwhile, I will build my new theory. However, now with another difference. The last time, I was content identifying the photon as a local condition, without specifying anything regarding its structure or the local dynamics. That was because, as a PhD student in engineering, I couldn’t afford to be too speculative. Now, however, I can afford to be a bit more relaxed, and begin considering toy ideas for more detailed models for the quanta. Inasmuch as photons are massless and there is aether, the situation is ripe for me to toy with some fluids-based ideas or models. Since I anyway do CFD, no one in engineering would even notice what I was doing was toying with some QM-related ideas. … Nice, no?

* * * * *   * * * * *   * * * * *

Anyway, best wishes for a merry Christmas, and a very happy and prosperous new year. … No, I don’t think I will be writing any post in the remaining parts of this year. So, there. Wish you a very happy and prosperous new year, too…

* * * * *   * * * * *   * * * * *

A Song I Like:

(Hindi) “jalate hain jis ke liye…”
Singer: Talat Mahmood
Music: S. D. Burman
Lyrics: Majrooh Sultanpuri

[As usual, I may come back and do some minor copy-editing and additions, though the main matter will remain as is. [Update on 2014.12.28: Done. I won’t bother any more with this post. If anything more is to be added, I will simply write a fresh post.]]

[E&OE]

Advertisements

An Important Comment I Just Made at iMechanica—And, (Much) More!

0. The title says it all!

Go, check out this comment I just made at iMechanica: [^].

1. Now, on to the “more” part of the title. Noted below are a few more things about my research.

2. My Researches on QM:

2.1 Since the publication of my QM-related results, I have moved on considerably further. As mentioned earlier on this blog, I have since then realized that my approach—the way I thought about it, as in contrast to what I (happened to have) published—always could handle the vector field equations of electromagnetism, including those for light. That is, including the angular momentum part of the EM fields. (Paddy, Suku, are you listening?) … However, I decided against publishing something in more detail to cover this aspect. A good decision, now it seems in retrospect.

(Yes, Jayant, you may now try your best to prod me towards publishing, including emphasizing how unpublished research is non-existent research. Just try it! Any which way you wish. … Precisely just the way I don’t give a damn to wannabe physicists turning JPBTIs turning entrepreneurs, I also don’t give a damn to the Statism-entrenching advices coming off the Statism-entrenching scientists, esp so if they also are the State-revered ones. So, just try it!! Also others, like, say, Sunil!!!)

2.2 I had also resolved the entanglement issue, and have chosen not to publish about it. As I stated earlier here [^], Louisa Guilder reports that Bell’s inequality paper has garnered the highest number of citations in physics literature so far, an astounding 2,500. The paper # 2,501 (or greater, as of today) must have concluded that the entanglement issue cannot be resolved—possibly out of the position/conviction that there was nothing to be resolved.

So, basically, I have resolved what an enormous number of misguided (and, possibly outright stupid) people could cite but not resolve.

Aside: Of the hundreds of papers on this topic I have come across, I know of Dr. Joy Christian’s position to be most reasonable—and in my knowledge, only his. Now, there are some minor differences between what he says and what I have always known and never published. But these differences are, in a sense, minor. The important part—and aren’t we concerned only with the important things here?—is that I knew about it, and have deliberately chosen not to publish about it. (If holding this position makes it possible to tick me off via certain lists such those maintained by a John Baez or a Scott Aaronson, I couldn’t care less about it—and both (and all) of them, I suppose, should know/could get to know, how (I care so less about those lists).)

BTW, as a matter of progression in time, I had thought that the issue would have to be first resolved in the context of photons, not of electrons. I am not very sure about it, though. In any case, that was the sequence in which I did it. First, photons; then, electrons.

Go, try your best to prod me towards publishing something on it! Just try it!! … BTW, my resolution had happened years before I had publicly offered an Indian PhD physicist on a “LinkedIn” group that I could explain my results if she (or anyone else) could meet me in person at Pune. This public offer of mine has just ended, right now!…. So, go ahead! Just try it!!!

3. My Researches on Other Topics

3.1 I have had some definite ideas for research on other topics from computational science and engineering and allied fields (including a numerics). I have kept these aside for the time being, because many of these are well-suited for guiding PhDs. Which brings me to the last couple of points for today (or at least, as of now, in the first version of this post).

3.2 As to student projects, I have decided not to accept anyone unless he is remarkably bright, and hard-working. (For those who seek to do truly independent PhD research, I cannot make myself available as a guide, as of now. Also see the point 3.3 below.) Roughly speaking, this means that rough level as would be understood by one or more of the following: GRE (V+Q) scores of at least 1350; GATE score of 95+P; throughout distinction class (or in at least 5 semesters out of 8) in BE of University of Pune (or equivalent).

3.3 The University of Pune has a stupid requirement for becoming a PhD guide: you (i.e. a fresh PhD graduate) must wait for at least 3 years after his own (successful) defense before he can become a PhD guide himself. The three years, in my case, end on September 20, 2012. (They—the Indian government(s)—probably arranged the date to numerically coincide with the date on which I first entered USA: 2nd September, 1990. Yes, the same government that whispered the UK government to give Rahul Gandhi’s brother-in-law all security clearance at UK airports, on par with the President and Prime Minister of India.)

Recently, someone reminded me a further requirement that I had forgotten. You also need to have two publications in those three years, before you can become a guide. Since I have mentioned the Gandhi’s and the defence-date here, I am sure that they would now interpret the sufficiently vague rules to imply that those two must be journal articles—peer-reviewed conference proceedings won’t do.

I, therefore, have decided to try to publish two journal articles in the near future of a few months. (Hey Elsevier, take notice!)

At least one, and probably both of these two articles would be on CFD.

Those of you who know me, would know that once I get going, I get going. I don’t disappoint (these of) you, not this time around at least: I have already installed Ubuntu 11.10 (natty) inside Oracle’s VirtualBox running on top of Windows (32 bit XP and 64-bit 7), and have already installed OpenFOAM v. 2.0.1 in that Ubuntu (32-bit, as of now). I also have installed other software. I have shortlisted the niche problems I could work on. I have contacted a couple of IIT Bombay professors, not for collaboration, but merely for sounding out. I knew that being employed by the IIT Bombay, there would be no collaboration, though a collaboration could have been perfectly OK by me. I also knew that once I wrote an email to them, it would get trapped (as all my emails are), and then, even the sounding things out over a 30 minute session would soon become impossible. And, that the impossibility would never be communicated explicitly via any means, esp. via an email. This  supposition of mine has indeed come to pass. (Congratulate me for being a good judge of the IIT Bombay, of the Indian government(s)—all of them, today’s and those of the past under the BJP regime as well, of Indians, and of humanity in general.) I knew all that, right in advance, and had prepared myself mentally for it. And, thought of plans B and C as well. I am executing on these.

And, no, I couldn’t care a hoot for how many freaking citations those two journal papers generate. As far as I am concerned, these two papers would allow me to fulfill the stupid requirements whereby I can become a PhD guide. And whereby, a slim chance does exist that I might get some good guy (gals included) for PhD supervision. (Chances are, it could be someone I already knew as a friend—numerically speaking, most of my friends are without PhDs.)

So, there. For the next few months, that’s the sort of research I am going to do—in my spare time, of course. Hey Elsevier, take notice (once again!!). As to others: If you consider yourself my friend, help me publish it in an easy and timely manner, ASAP.

That’s all for today. For this first version, anyway. As always, I might come back and correct or add a few things. …. Might as well add a few political comments right here.

4. A Few Comments on Politics and All:

Just noting down a few comments on politics (i.e. that politics which is “larger” than the one in S&T fields) in passing (and I will take liberties to pass comments on people without alerting them):

To ObjectivistMantra and Others:

Tavleen Singh’s article on the slap to Mr. Pawar was the best. However, it fell short on the count of completeness. On this count of completeness, she does far, far better (actually excellent) with her next article in the Indian Express’ Fifth Column. Why I say she fell short. In an entrenched mixed economy such as ours (i.e. India’s as in the past and as of today, and of USA’s in near future), the whole system has already become so statist, so mangling of individual rights, that it is impossible to systematically assign blame on any one systemic part of it. In my twenties and early thirty’s (i.e. 15–25 years ago), having known this, I used to argue that it would be impossible for the Indian army (i.e. defence services in general) or the Indian courts to be singled out as being clean. Time proved me right. Indeed, it’s at least since my X standard (i.e. for ~35 years now) that I have argued that you can’t blame politicians—indeed that far too many politicians, from the village through the national level enjoyed much more of esteem in my opinion than what salaried class (say, my “Brahmin” friends) would allow them. Sometime while I was in SF Bay Area, I further realized that the trend to say: “It’s all polltishuns; common people and businessmen are clean” had originated not in India, but in the middle-east and Pakistan etc., and that our Punjabi’s, Gujarathi’s etc. settled in the USA and UK (e.g. Kanwal Rehi, Vinod Khosla and their friends there and here) had been simply rubbing the characterization (actually applicable in the middle-east and Pakistan etc.), expectedly witlessly, on to India’s scene. Since Shobha Dey makes many frequent visits to Dubai, she was expected to have picked it up, too. And, she has shown over the years  that she has. Her latest column springs from that faulty position as regards India. Tavleen Singh is better. (That’s one basic reason why a link to her columns features in the my blogroll here.) Singh did stop short of stretching on that line. However, she did get overwhelmed by the dominant presence of that erroneous idea in our present culture. That’s why, she couldn’t think of a single example on the following lines: Taking a symmetrical case, should I be allowed to put a slap on the face of a Kanwal Rekhi or a Vinod Khosla, for not giving me a job in SF Bay Area in late 2000/early 2001, so that my green-card processing could have been completed? Should I be permitted—morally, even if not legally—to land a (Marathi) “saNsaNit thappaD” (nearest English: a resounding slap) on the face of a Ratan Tata, not just for never giving a job in his company (in Ratan’s case, Tatas) but even allowing my harassment (e.g. as stated on a LinkedIn thread re. VSNL/Tata Indicom Broadband)? Would it be morally justifiable? Why, Ms Tavleen, speak of the emotions of common man but refuse to discuss the issue on more clearly and more on specifically moral terms? So, you see, even if Ms. Singh is far better—and here I thankfully recall all her wonderful articles in the recent past, esp. the courage she has shown in taking on the urban twittering “middle” classes in the “Gandhian” Anna Hazaare “movement”—it is obvious that she overlooked something. Mind you, it’s just plain omission (and as far as I am concerned, it seems to be a very honest one). But still, an error is an error. On omission is an omission. Since I enjoy and admire her columns as much as you do, I hope that she addresses the moral aspects of the emotional issues rather than emotions. In any case, what she wrote was otherwise far better, far superior to what I could have written. This is exactly like Swapan Dasgupta’s recent article. Except for that one error, the rest of the article is excellent! But, hey, you don’t design or manufacture 99 components of an engine well, and leave 1 component out of either good design process or actual testing. As to Ms. Dey, I think I am going to stop reading her now. Some time ago, she was wondering when certain people had kissed last, in the context of—and who else: Indian “poltishun”s. (In case someone finds it intriguing, realize that she is a daughter of an Indian central bureucrat, and as far as I can make it out, has had no explicit rational philosophy to guide her writings, though she is a lady of enormous culture and composure in her own right too. Oh well, even explicit rational ideas do make a difference—think what a whole rational philosophy can do!)

I think I will stop here, and add possibly add other points via other blog posts. For the time being, as far as politics goes, I am enjoying (“loving it”) watching the BJP more than anyone else in the opposition/government, as far as the issue of retail FDI goes.  However, I am not going to support Walmart for the simple reasons that (i) their country has unreasonably failed me in the PhD and unreasonably denied me green-card/citizenship, (ii) they are too big to need my support anyway, and (iii) supporting a big company against government—Microsoft, in the DoJ case—was one among many things that got me a heart condition, I know. (How do I know? Well, it’s the same guy who has known how to resolve the QM wave-particle duality in the context of light, and about angular momentum in EM, and then, a resolution of the riddles of quantum entanglement, as well as many other unpublished, even un-discussed topics.)

One final point, again going back towards research. For the past several years I could not fathom the reason why people might be so unenthusiastic about my approach—I mean, honest people (apart from all the dirty things and “political” issues I have mentioned/indicated above.) Well, it was while reading Sean Carroll’s blog at Discovery magazine that I happened to realize one important (technical) reason why this might be (or must be) so! Hmmm…. Nice to know. It’s always great to know. Though, I am not going to divulge here what that thing was—or how it not only doesn’t contradict my approach but rather helps me be even more confident about my approach (if I ever needed such help, in this context!) And, as you know, I am not going to discuss it or publish about it either. Try to get me to do otherwise. … Just try!
Ok. Enough is enough. As usual, to be edited/streamlined later—perhaps!

* * * * *   * * * * *   * * * * * 
A Song I Like:
[RIP, Dev Anand!]
(Hindi) “gaataa rahe, meraa dil…”
Music: S. D. Burman (perhaps with R.D. looking after the orchestra (??) if not also the tune. (I have read somewhere that he was involved in “Aaraadhanaa,” but have no such idea when it comes to “Guide”)
Singers: Kishore Kumar, Lata Mangeshkar
Lyrics: Shailendra

[E&OE]